The Cherries have struggled so far this season and they're currently second-bottom of the Premier League with just four points and one win from seven games.
However, Begovic believes they will soon get wins on the board and they will be rewarded with the points their displays deserve.
He told the Daily Echo: "I think our performances over the past month or so have showed we are a good team and a tough team to play against when we are all on it.
"If a couple of things click, we will be on a great run and we will push up the table.
"We are pleased with how we are playing. Little moments decide games and those things are missing right now but, overall, the performances are solid and everyone is getting better and stronger each and every game.
"I think if we keep playing like this and show a bit of consistency in the performances, then we will start picking up wins."
Bournemouth take on Spurs on Saturday when the league action resumes following the international break.